The present invention relates to fast random access methods and arrangements for the enhanced uplink dedicated channel of E-UTRAN (Evolved Universal terrestrial radio access network). A user equipment (UE) being in a low activity state sends a random access request comprising a preamble on a physical random access channel (PRACH) to a NodeB. The NodeB receives the request and sends in response to the received random access request a response comprising information associated with detection of the preamble on an acquisition indicator channel (AICH). The response comprises further in an extension of the AICH an indication of an action to be taken by the UE. In an embodiment of the present invention the action is to access the E-DCH and the response comprises configuration parameters to the E-DCH.